Showing papers on "Timoshenko beam theory published in 1991"
TL;DR: In this article, a general beam theory has been proposed which is applicable to all regular prismatic systems and is used to find the appropriate beam-like flexibilities for trusses.
84 citations
TL;DR: In this paper, a thin-walled box-girder finite element that can model extension, flexure, torsion, distortion, distortional warping, and shear lag effects was developed using an extended version of Vlasov's thinwalled beam theory.
Abstract: A thin‐walled‐box‐girder finite element that can model extension, flexure, torsion, torsional warping, distortion, distortional warping, and shear lag effects was developed using an extended version of Vlasov's thin‐walled beam theory. The element has two end nodes, but it has besides the six nodal degrees of freedom of a conventional beam element, additional degrees of freedom to account for torsional warping, distortion, distortional warping, and shear lag. The governing differential equation pertaining to each action was used to derive the exact shape functions and the stiffness matrix and nodal load vector of the element. An orthogonalization procedure was employed to uncouple the various distortional and shear lag modes. A numerical example was solved that compared the proposed method with the facet‐shell finite element analysis, with good agreement between the two sets of results.
61 citations
TL;DR: In this article, a systematic reduction of the constitutive relations of the three-dimensional anisotropic body of a composite beam has been considered by using the parabolic shear deformation theory, and numerical results for natural frequencies and the Euler buckling load have been presented.
57 citations
TL;DR: In this paper, a new set of state variables, composed of Cartesian co-ordinates of points and unit vectors, is introduced to define the beam with respect to an inertial frame.
Abstract: A formulation for the dynamic analysis of flexible systems, composed of slender bodies that can be accurately modelled by beams is presented in this paper. A new set of state variables, composed of Cartesian co-ordinates of points and unit vectors, is introduced to define the beam with respect to an inertial frame. A non-linear Timoshenko beam finite element capable of handling finite displacements with small linear elastic strains is developed. This allows relative displacements between material points of a single beam to be arbitrarily large. Since deformations are not explicit variables, there is no need to define a moving reference frame attached to each flexible body. Instead, deformations are obtained through a displacement-deformation relation based on finite-displacement beam theory. The differential equations of motion are obtained using the Lagrange equations. A symmetric, constant and sparse mass matrix is obtained in the inertial frame. Constraints are introduced with a penalty formulation and the resulting set of ordinary differential equations is integrated with Newmark's family of methods. The whole formulation is extremely simple and the results demonstrate the capabilities and efficiency of the proposed method for dynamic simulation, even when relative displacements are finite in a single beam or coupling effects are significant.
56 citations
TL;DR: In this article, the effect of the shear stiffness on column buckling load for the usual standard boundary conditions is also presented analytically, and in the form of graphs.
Abstract: The buckling of columns with finite shear stiffness such as built-up and laced columns is investigated. The methods of analysis associated with Engesser and Haringx are compared. The difference between the methods can be traced to the direction of the axial force and the shear force used in the analysis. It is concluded that when the usual shear stiffness of the column is used, the Engesser method is the correct one for columns modeled as continuous Timoshenko shear beams. The appropriate method to use for helical springs is not investigated. The effect of the shear stiffness on the column buckling load for the usual standard boundary conditions is also presented analytically, and in the form of graphs.
52 citations
TL;DR: In this paper, a rotating Timoshenko shaft with a single transverse crack is considered, where the crack opens and closes during motion, and the six coupled, piecewise-linear equations of motion are integrated numerically after application of Galerkin's method with two-term approximations for each of the six displacements.
Abstract: A rotating Timoshenko shaft with a single transverse crack is considered. The crack opens and closes during motion. The shaft has simply supported ends, and the six coupled, piecewise-linear equations of motion are integrated numerically after application of Galerkin's method with two-term approximations for each of the six displacements. Time histories and frequency spectra are compared for shafts with no crack and with a crack
51 citations
TL;DR: In this paper, a flexible spacecraft modelled as a rigid body which rotates in an inertial space is considered; a light flexible beam is clamped to the rigid body at one end and free at the other end.
Abstract: A flexible spacecraft modelled as a rigid body which rotates in an inertial space is considered; a light flexible beam is clamped to the rigid body at one end and free at the other end. The equations of motion are obtained by using the geometrically exact beam model for the flexible beam, and it is then shown that under planar motion assumption, linearization of this model yields the Timoshenko beam model. It is shown that suitable boundary controls applied to the free end of the beam and a control torque applied to the rigid body stabilize the system. The proof is obtained by using a Lyapunov functional based on the energy of the system.
50 citations
TL;DR: In this paper, a finite element procedure is developed for analyzing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation, which is discretized into a number of simple elements with four degrees of freedom each.
Abstract: A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.
50 citations
43 citations
TL;DR: In this paper, the Timoshenko beam elements are used to analyze vibration and stability of fluid conveying pipes, and the theoretical background is presented and results are compared with results obtained by Paidoussis et al.
39 citations
TL;DR: In this article, a simple theory for the coupled warping and cross-sectional distortion at joints between thin-walled I-beams is developed, where the distortion mode acts as a local spring stiffness.
Abstract: A simple theory is developed for the coupled warping and cross-sectional distortion at joints between thin-walled I-beams. Continuity of the joined flanges and the local character of the cross-sectional distortion permit the distortion deformation to be expressed in terms of the warping parameters of the two beams at the joint. Four types of joints are treated. The unstiffened joint has two independent warping parameters, the two partially stiffened joints each have a single warping parameter, while the fully stiffened joint prevents warping. The distortion mode acts as a local spring stiffness. The formulation is fully compatible with classical thin-walled beam theory, and detailed three-dimensional finite element analyses demonstrate high accuracy of the theory.
TL;DR: In this article, the authors investigated the compliance and strain energy release rate of homogeneous and interleaved end-notched flexure specimens for mode II fracture characterization with shear deformation beam theory and finite element analysis.
Abstract: Compliance and strain energy release rate of homogeneous and interleaved end-notched flexure specimens for mode II fracture characterization are investigated with shear deformation beam theory and finite element analysis. Interleaving refers to a thin layer of polymer film being placed at the midplane of the beam. Analytical results are correlated with numerical finite element results for a wide range of interleaf thicknesses. The finite element results revealed that the compliance and energy release rate remained virtually the same whether the crack was within the interlayer or between the interlayer and the composite. Furthermore, within the accuracy of the numerical modeling, the asymmetric crack configuration did not render the specimen mixed mode, (GI=0). Close agreement was observed between sandwich beam theory and finite element analysis.
TL;DR: In this paper, a method of analysis for beams with shear-lag effects from wide flanges and shear deformations resulting from shear studs in composite beams is presented.
Abstract: A method of analysis for beams with shear-lag effects from wide flanges or with shear deformations resulting from shear studs in composite beams is presented. The basic idea is to replace the real beam with an analog beam, where all the shear deformation is concentrated in a thin layer. The equivalent stiffness of the shear layer can be related to the properties of the flange and the shear studs connecting the beam and the slab. When this stiffness is assigned to shear layer, the real beam and its analog behave in the same overall manner. The solution to the analog beam problem is directly related to the deformation and stresses in the real beam through simple formulas. The method is more complicated, but also more accurate than the customary effective width method, and could prove a good tool for design purposes.
TL;DR: In this article, beam theory and the J-integral and the principle of superposition in a linear elastic body were used to calculate the mode I and mode II stress intensity factors in a generic cracked adhesive sandwich.
TL;DR: In this article, the governing nonlinear finite element equations for the spatial stability analysis of curved beams, using a simple two-noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross-sectional warping and bending/twisting rotations.
Abstract: The governing non-linear finite element equations for the spatial stability analysis of curved beams, using a simple two-noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross-sectional warping and bending/twisting rotations. The formulation is valid for both open-and closed-type thin-walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural-and warping-torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second-order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral-torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations.
TL;DR: In this article, Vlasov's thin-walled beam theory is combined with special shear lag warping functions to derive a box beam finite element with exact shape functions which can be used to analyze single and multi-cell box girders.
TL;DR: In this paper, the problem of free vibration of uniform beams containing a local material damage has been studied with the aim of arriving at accurate closed form analytical expressions for the natural frequency for various homogeneous boundary conditions.
TL;DR: In this article, the effects of transverse shear on the flexural vibrations of free beams were studied and the analysis was based on Timoshenko beam theory, the accuracy of which has been studied by making comparisons with results from finite element calculations.
TL;DR: In this paper, a three-nodal, C 0 Timoshenko beam finite element model is applied to analyze the natural whirl speeds of a rotating shaft with different end conditions.
TL;DR: In this paper, the authors presented a systematic derivation of a refined engineering theory governing the response of elastic beams using asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the linear elasticity theory.
Abstract: A systematic derivation of a refined engineering theory governing the response of elastic beams is presented. The method employed to accomplish this is that of asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the three-dimensional linear elasticity theory. The present beam theory contains more information than the classical Timoshenko theory. A new shear coefficient is defined and compared with existing ones.
TL;DR: In this article, the Timoshenko beam problem is examined under the gênerai hypotheses of Brezzi's theorem concerning existence and uniqueness of saddle point problems, and a new finite element approximation is proposed and shown to be convergent for varions combinations of interpolations for the three variables.
Abstract: — The Timoshenko beam problem, with shear for ce and rotation as primai variables and displacement as Lagrange multiplier, is examined under the gênerai hypotheses of Brezzi's theorem concerning existence and uniqueness of saddle point problems. A new finite element approximation is proposed and shown to be convergent for varions combinations of interpolations for the three variables. Résumé. — Le problème de la poutre de Timoshenko, avec pour variables primales la force de cisaillement et la rotation, et comme multiplicateur de Lagrange le déplacement, est examiné sous les hypothèses générales du théorème de Brezzi relatives à l'existence et l'unicité des problèmes de points-selles. Une nouvelle approximation par éléments finis est proposée ici, et nous prouvons la convergence pour des combinaisons variées d'espaces d'interpolation sur les trois variables.
TL;DR: In this paper, the stability behavior of a Timoshenko beam subjected to a uniformly distributed follower force is studied by the finite element method in order to more quickly and efficiently obtain the critical load for such a system, a technique which utilizes the eigenvalue sensitivity with respect to the nonconservative force is introduced instead of the conventional trial and error technique.
TL;DR: In this paper, a linear partial differential equation describing the motion of the Timoshenko beam with viscous internal dampings and with a certain type of boundary inputs is formulated as an evolution equation of the form dz( t)/dt = Az( i) in a Hilbert space, and then it is proved for the linear operator A to generate an analytic semigroup.
Abstract: This paper is concerned with the linear partial differential equation describing the motion of the Timoshenko beam with viscous internal dampings and with a certain type of boundary inputs. The equation is formulated as an evolution equation of the form dz( t)/dt = — Az( i) in a Hilbert space, and then it is proved for the linear operator — A to generate an analytic semigroup. Moreover, the stability of the boundary control system is examined. It is shown that in some cases the present type of boundary inputs degrades the degree of stability of the system. This is a remarkable contrast to the results of previous research which states that the same type of boundary inputs are effctive in stabilizing the Timoshenko beam without any structural damping.
TL;DR: In this paper, the convergence of one difference equation gives an interpretation of the source of troubles occurring in low-order bending elements which is more convincing than the usually applied consideration of the conditioning of element stiffness matrices.
Abstract: A new methodology of evaluation of C0 beam elements is presented. It is shown that, knowing the stiffness matrix of an arbitrary type of element, it is possible to create equivalent equilibrium conditions expressed in the form of one difference equation for a regular beam discretized by these elements. The study of the convergence of one difference equation gives an interpretation of the source of troubles occurring in low-order bending elements which is more convincing than the usually applied consideration of the conditioning of element stiffness matrices. A careful examination of quadratic Mindlin elements provides a very clear explanation of the shear locking essence in the Timoshenko beam. The presented method enables one to identify errors that appear also in the reduced integrated or constrained elements. For each type of analysed quadratic element an adequate difference equation is derived and compared with the exact one. Based on this comparison a simple method of corrections is proposed that completely eliminates the errors associated with the application of C0 bending elements.
TL;DR: In this paper, the authors used Engesser's approach for the shearflexural buckling analysis of continuously restrained columns and derived the total potential energy functional, which forms the basis of the finite element method for solution.
Abstract: There are two well‐known approaches proposed for incorporating shear deformation in the analysis of column buckling. Engesser's approach assumes that the shear component acts perpendicularly to the total slope while Haringx's approach assumes that it acts perpendicularly to the bending slope. It appears that discussions are still going on as to which of the approaches is more accurate. It is doubtful if the problem can be resolved through mechanics, as Reissner had pointed out that the approaches depend on the form of the assumed, one‐dimensional, stress‐strain relations. This paper will use Engesser's approach for the shearflexural buckling analysis of continuously restrained columns. The effect of axial shortening is also considered. A derivation is presented for the total potential energy functional, which forms the basis of the finite element method for solution. A parametric study is carried out to investigate sensitivity to various design parameters.
Journal Article•
TL;DR: In this article, a C 0, three-node isoparametric finite element model is developed to study the whirl speeds of a rotor-bearing system with both internal viscous and hysteretic damping.